Consider the pattern.
$\displaystyle 5^3=125$
$\displaystyle 5^4=625$
$\displaystyle 5^5=3125$
$\displaystyle 5^6=15625$
Use this pattern to write out the last 3 digits of $\displaystyle 5^{15} $.
How can I work this out?
Consider the pattern.
$\displaystyle 5^3=125$
$\displaystyle 5^4=625$
$\displaystyle 5^5=3125$
$\displaystyle 5^6=15625$
Use this pattern to write out the last 3 digits of $\displaystyle 5^{15} $.
How can I work this out?
1. You do not specify how many digits constitute "the last" digits of $\displaystyle 5^{15}$.
2. A suitable hypothesis might be that the last two digits of $\displaystyle 5^n$ for $\displaystyle n\ge 2$ are $\displaystyle 25$.
3. Suppose this true for $\displaystyle k$ that is $\displaystyle 5^k=100 \times M+25$ for some integer $\displaystyle M$, now $\displaystyle 5^{k+1}= ...$
NOw can you take it from there?
CB